Unit Conversions Volume

Look at the table below and memorize the metric conversions of all units used to measure length.

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Common Volume Conversion Factors

1 cubic centimeter =

1000 cubic millimeter

1 cubic decimeter =

1000 cubic centimeter

1 cubic meter =

1000 cubic decimeter

1 liter / litre =

.001 cubic meter

1 liter / litre =

10 deciliter

1 deciliter =

10 centiliter

1 centiliter =

10 milliliter

1 cubic foot =

1728 cubic inches

1 cubic yard =

27 cubic feet

1 fluid minims =

61.61152 cu mm

1 fluid drams =

60 minims

1 fluid ounces =

8 fluid drams

1 pint (pt) =

16 fluid ounces

1 gills (gi) =

0.25 pint

1 quart (qt) =

2 pint

1 gallon (gal) =

4 quart

1 oil barrel =

42 gallons


In order to convert metric units into English units and other units of measurements, we will use the
conversion factors stated above. Notice that we always use 1 unit of the length to be converted. Once this
is known, the conversion factor, we can then use this to multiply against a unit we wish to be converted.

REMEMBER

When going from a large unit to a small unit, you multiply.

When going from a small unit to a large unit, you divide.

There is another way of converting units. It is often called the long way because you need to arrange the values
to make a ratio and proportion equation. For example:

  1. If 1 gallon = 4 quarts, how many gallons will there be in 20 quarts?

    Answer:

    (1 gallon / 4 quarts) = (x gallons / 20 quarts)

    1 gallon x 20 quarts = 4 quarts

    X = 5 quarts


  2. Today, the price is 3.4 AED/liter. If Jessie filled up her car with 40 deciliter quarts of gasoline,
    (a) what is the volume she purchased in liters? (b) how much did she pay for this?

    Answer:

    (a) Convert dL to L

    (1 L / 10 dL) = (x / 40)

    (40 / 10) = 4 L

    b) (3.4 AED / L) = (x / 4)

    3.4 x 4 = x

    13.6 AED = x


  3. A pint of beer costs $8. Jack and his four friends bought 3 pints each.
    (a) How many quarts of beer did they consume in total? (b) How much did they pay in total?

    Answer:

    Total pint consumed = 12 pints

    a) (1 pint / 2 quarts) = (12 / x)

    x = 12 x 2

    x = 24 quarts

    b) 12 x 8 = $96

Try these questions

  1. A cough syrup has a dosage of 250 mg/5 mL of the prescribed antibacterial. The doctor calls for 750mg
    to be taken twice daily. What is the total volume to be taken?

    Answer: 30 mL

    Explanation:

    Use ratio and proportion first to find out the volume of one dose:

    (250 mg/5 mL) = (750 mg / x mL)

    x mL = 15 mL

    Twice daily: 15 mL x 2 = 30 mL total volume to be taken


  2. During renovation, the two painters used up 1/3 of the 10 pint red paint.
    How many fluid ounces of red paint were used up?

    Answer: 53.28 fluid ounce

    Explanation:

    1/3 x 10 pint = 3.33 pint

    Convert pint to fluid ounce

    (1 pint / 16 fluid ounces) = (3.33 pint / x)

    X= 16 fluid ounces x 3.33 pint

    X = 53.28 fluid ounce


  3. The sum of the lengths of all sides of a cube is 8 cm. What is its volume? (Volume = l x w x h).

    Answer: 2 cm

    Explanation:

    Since a cube has 12 sides, we get:

    12e = 8

    e = 8/12 or 2/3

    Therefore, its volume is: e3

    (2/3) x (2/3) x (2/3) =1.99 or 2 cm.


  4. Jessie diluted 3L of mango puree with 4340 mL of distilled water. What is the resulting volume of the
    mixture in mL?

    Answer: 7340 mL

    Explanation:

    Convert L to mL

    (1 L / 1000 mL) = (3L / x mL)

    X = 3000 mL

    Add the two volumes:

    3000 mL + 4340 mL = 7340 mL